Matlab學習與實驗教程-第5章 MATLAB數據分析與多項式計算

1、第5章 MATLAB數據分析與多項式計算例5-1 x=-43,72,9,16,23,47; y=max(x)%求向量x中的最大值y =72 yz 1 =max (x)%求向量x中的最大值及該元素的位置y =721 =2例5-2 x= 1,8,4,2; 9, 6, 2,5; 3, 6, 7,1x =184296253671 y=max(x) y =9875 yz1=max(x) y =98751 =2132 y, 1=max (x, ,1)x =184296253671 y=max(x) y =9875 yz1=max(x) y =98751 =2132 y, 1=max (x, ,1)%求矩陣

2、x中各列元素的最大值國求矩陣x中各列元素的最大值及這些元素的行下標%本命令的執(zhí)行結果與上面的命令完全相同y =98751 =2132 y,1=max(x,2) y =897=1 max(max(x)%命令中dim=2,故查找操作在各行中進行%求整個矩陣的最大值ans = min(min(x)%求整個矩陣的最小值ans =1例5-3 x= 4,5, 6; 1,4,8x = TOC o 1-5 h z 456148 y=l,7,5;4,5z7y =175%在x,y同一位置上的兩個元素中找出較大值457 p=max(x,y)P =476458例5-4 A=l,2,3,4;5,6,7,8;9,10,l

3、l,12; 乞求 A 的每行元素的乘積 S=prod(A,2)241680故求A的全部元素的乘積故求A的全部元素的乘積11880 prod(S)ans =479001600例5-5 x=9,-2,5,7,12; mean(x)ans =6.2000 median(x)ans =7 y=9,-2,5,6,7,12; mean(y)ans =6.1667 median(y)ans =6.5000例5-6 x=1,ones(1,10)*2x =1222%奇數個元素%偶數個元素222222 y=cumprod(x)127至11列64128 s=sum(y)s =2047例5-7 x= 4,5, 6;

4、1,4,8; yl=std(x,0,1)yi =2.12130.7071 vl=var(x,0,1)vl =4.50000.5000 y2=std(xz1,1) y2=1.50000.5000 v2=var(x,1,1)v2 =2.25000.2500 y3=std(x,0,2) y3=1.000048256512%求標準差1.4142%求方差2.00001.00001.0000163210243.5119 v3=var(xz 0,2) v3 =1.000012.3333 y4=std(x,1,2) y4 =0.81652.8674 v4=var(xz1z 2) v4 =0.66678.222

5、2例5-8 X=randn(10000z 5);M=mean(X)M =0.0017-0.0020-0.0038 D=std(X) D =0.99150.98990.9995-0.0001-0.01060.98621.0118 R=corrcoef(X)R =1.00000.0060-0.00010.01110.00051.00000.0060-0.00010.01110.00050.00601.0000-0.0030-0.0131-0.0050-0.0001-0.00301.0000-0.0203-0.00240.0111-0.0131-0.02031.00000.01220.0005-0.

6、0050-0.00240.01221.0000sort(A)%對A的每列按升序排序例5-9A=l,-8,5;4,12,6;13,7,-13;ans sort(A,2, descend1) sort(A,2, descend1)對A的每行按降序排序ans =51-81264137-13 XzI=sort(A)X =1-8-1347513126I =113231322例 5-10 X=0:0.2:pi;Y=sin(X); interpl(X,Y,pi/2)ans =51-81264137-13 XzI=sort(A)X =1-8-1347513126I =113231322例 5-10 X=0:0

7、.2:pi;Y=sin(X); interpl(X,Y,pi/2)%對A按列排序，并將每個元素所在行號送矩陣工%給出X、Y%用默認方法(即線性插值方法)計算sin (n/2)ans =0.9975 interpl(X,Y,pi/2, 1 nearest1) ans =0.9996 interpl(X,Y,pi/2,linear) ans =0.9975 interpl(X,Y,pi/2, 1pchip *) ans =0.9992 interpl(X,Y,pi/2, 1 spline 1) ans =1.0000ans =0.9975 interpl(X,Y,pi/2, 1 nearest1)

8、 ans =0.9996 interpl(X,Y,pi/2,linear) ans =0.9975 interpl(X,Y,pi/2, 1pchip *) ans =0.9992 interpl(X,Y,pi/2, 1 spline 1) ans =1.0000義用最近點插值方法計算sin (n/2)%用線性插值方法計算sin (n/2)號用3次Hermite插值方法計算sin (n/2)%用3次樣條插值方法計算sin (n/2)1-8-1347513126例 5-11 h =6:2:18; t=18,20,22,25,30,28,24;15,19,24,28,34,32,30， XI =6.

9、5:2:17.5XI =6.50008.500010.5000 YI=interpl(h,t,XI, 1 spline)YI =6.50008.500010.5000 YI=interpl(h,t,XI, 1 spline)YI =12.500014.500016.5000留用3次樣條插值計算18.502020.498622.519326.377530.205126.817818.502020.498622.519326.377530.205126.817815.655320.335524.908929.638334.256830.9594例 5-12%產生自變量網格坐標%求對應的函數值%在（

10、05,0.5）點插值%在（05,0.4）點和（0.6, 0.4）點插值0.5 )%在(05, 0.4)點和(0.6, 0.5)點插值 x=0:0.1:1;y=0:0.2:2; X,Y=meshgrid(xz y); Z=X.人2+Y.人2; interp2(x,y,Z,0.5,05)ans =0.5100 interp2(xzyzZ,0.5 0.6,0.4)ans =0.41000.5200 interp2(x,y,Z,0.5 0.6,0.4ans =0.41000.6200以下命令在(05 0.4) (0.6, 0.4) (0.5, 0.5)和(06 0.5)各點插值。 interp2 (x

11、,y,Z, 0.5 0.6 1r 0.4 0.5)ans =0.41000.52000.51000.6200如果想提高插值精度，可選擇插值方法為spline：對于本例，精度可以提高。輸入命令: interp2(x,y,Z, 0.5 0.6 1, 0.4 0.5, * spline 1)ans =0.41000.52000.50000.6100例 5-13 x=0:2.5:10; h=0:30:60 T= 95, 14,0, 0,0; 88,4 8,32,12,6; 67, 64,54,4 8,41; xi=0:10; hi=0:20:601; TI=interp2(x,h,T,xi,hi)TI

12、 =1至7列5.600095.000062.600030.200011.200090.333381.000090.333381.000068.866769.933347.400058.866767.00008至11列065.8000064.6000033.600050.533362.000027.466744.933358.000021.333339.333354.000016.000033.200051.600010.666727.066749.20007.200022.733346.60005.600020.200043.800004.000017.666741.0000例 5-14 t=

13、l:10; y=9.6,4.l,1.3,04,005,0.l,07,l.8,38,9.0; p=polyfit (t, y, 2)%計算2次擬合多項式的系數P =0.4561-5.041213.2533以上求得了 2次擬合多項式p(t)的系數分別為0.4561、-5.0412 13.2533,故p(t)= 0.4561t2-5.0412t+13.2533o以下再用polyval求得ti各點上的函數近似值： ti=l:0.5:10; yi=polyval(p,ti) yi = 1至7歹U8.66826.71774.99523.50072.23421.19580.38558至14列-0.1969-

14、0.5512-0.6775-0.5758-0.24600.31181.097715至19列 2.11153.35344.82336.52138.4473根據計算結果可以繪制出擬合曲線圖，命令如下： plot(t,yz1:of,ti,yi,*)例 5-16 A= 1,8,0,0,TO; B=2Z-1,3; C=conv(A,B) C = 215-524-2010-30例 5-17 A=l,8,0,0,-10; B=2,-1,3; P,r=deconv(A,B) P = 0.50004.25001.3750r = 000 -11.3750 -14.1250150 5-18 p=1; Q=1,0,5

15、; Pz q=polyder(P, Q)-2q =1010025例 5-19 A=lz8,0z0,-10 ;% 4 次多項式系數 x=1.2;%取自變量為一數值 yl=polyval(A,x) yi =5.8976 x=-lz1.2,-1.4;2z-1.8,1.6% 給出一個矩陣 x-1.00001.2000-1.40002.0000-1.8000 y2=polyval(A,x) y2 =-17.00005.897670.0000 -46.15841.6000%分別計算矩陣x中各元素為自變量的多項式之值-28.110429.3216例 5-20 A=l,8,0,0,-10; x=-1,1.2;2Z-1.8 x =-1.00001.20002.0000-1.8000 yl=polyval(A,x) yi =-17.00005.897670.0000 -46.1584 y2=polyvalm(A, x) y2 =-60.584050.6496%多項式系數%給出一個矩陣x%計算代數多項式的值%計算矩陣多項式的值84.4160 -94.3504例 5-21 A=1,8,0,0,-10; x=roots(A)-8.0194-8.0194+ O.OOOOi1.0344 + O